/// <summary>
/// de Casteljau's algorithm for exactly 3 points
/// </summary>
private static GlyphPoint InterpolatePoints([NotNull] GlyphPoint start, [NotNull] GlyphPoint ctrl, [NotNull] GlyphPoint end, double t, double it)
{
var aX = it * start.X + t * ctrl.X;
var aY = it * start.Y + t * ctrl.Y;
var bX = it * ctrl.X + t * end.X;
var bY = it * ctrl.Y + t * end.Y;
return(new GlyphPoint {
X = it * aX + t * bX,
Y = it * aY + t * bY
});
}
/// <summary>
/// A more refined curve breaker for larger sizes
/// </summary>
[NotNull] private static IEnumerable <GlyphPoint> InterpolateCurve([NotNull] GlyphPoint start, [NotNull] GlyphPoint ctrl, [NotNull] GlyphPoint end)
{
// Estimate a step size
var dx1 = start.X - ctrl.X;
var dy1 = start.Y - ctrl.Y;
var dx2 = ctrl.X - end.X;
var dy2 = ctrl.Y - end.Y;
var dist = Math.Sqrt((dx1 * dx1) + (dy1 * dy1) + (dx2 * dx2) + (dy2 * dy2));
if (dist <= 1)
{
yield return(start);
yield break;
}
var minStep = 20.0d; // larger = less refined curve, but faster
var inv = minStep / dist; // estimated step size. Refined by 'minStep' checks in the main loop
for (double t = 0; t < 1; t += inv)
{
yield return(InterpolatePoints(start, ctrl, end, t, 1.0 - t));
}
}
/// <summary>
/// break curves into segments where needed
/// </summary>
[NotNull] public static GlyphPoint[] NormaliseContour([NotNull] IReadOnlyList <GlyphPoint> contour)
{
var len = contour.Count;
var final = new List <GlyphPoint>(len * 4);
var offs = len - 1;
// If we get more than one 'off-curve' point in a row,
// then we add a new virtual point between the two off-curve
// points, and interpolate a bezier curve with 1 control point
for (int i = 0; i <= len; i++)
{
var current = contour[i % len];
var prev = contour[(i + offs) % len];
var next = contour[(i + 1) % len];
if (current == null || prev == null || next == null)
{
throw new Exception($"Invalid contour at point {i}");
}
// if current is on-curve, just add it.
// if current is off-curve, but next is on-curve, do a simple interpolate
// if current AND next are off-curve, create a virtual point and interpolate
if (current.OnCurve) // simple corner point
{
final.Add(current);
}
else if (next.OnCurve && prev.OnCurve) // simple curve
{
final.AddRange(InterpolateCurve(prev, current, next));
}
else if (prev.OnCurve) // single virtual curve forward
{
var virt = new GlyphPoint
{
X = (current.X + next.X) / 2.0,
Y = (current.Y + next.Y) / 2.0
};
final.AddRange(InterpolateCurve(prev, current, virt));
}
else if (next.OnCurve) // single virtual curve behind
{
var virt = new GlyphPoint
{
X = (current.X + prev.X) / 2.0,
Y = (current.Y + prev.Y) / 2.0
};
final.AddRange(InterpolateCurve(virt, current, next));
}
else // double virtual curve
{
var virtPrev = new GlyphPoint
{
X = (current.X + prev.X) / 2.0,
Y = (current.Y + prev.Y) / 2.0
};
var virtNext = new GlyphPoint
{
X = (current.X + next.X) / 2.0,
Y = (current.Y + next.Y) / 2.0
};
final.AddRange(InterpolateCurve(virtPrev, current, virtNext));
}
}
return(final.ToArray());
}